Multilevel Non-Linear Random Effects Claims Reserving Models and Data Variability Structures

Characteristic of many reserving methods designed to analyse claims data aggregated by contract or sets of contracts, is the assumption that features typifying historical data are representative of the underwritten risk and of future losses likely to affect the contracts. Kremer (1982), Bornheutter and Ferguson (1972), de Alba (2002), and many others, consider models with development patterns common to all underwriting years and known mean-variance relationships. Data amenable to such assumptions are indeed rare. More usual are large variations in settlement speeds, exposure and claim volumes. Also typifying many published models are Incurred But Not Reported (IBNR) predictions limited to periods with known claims, frequently adjusted with "tail factors" generated from market statistics. Of concern could be analytical approach inconsistencies behind reserves for delay periods before and after the last known claims, under reserving and unfair reserve allocation at underwriting year, array or contract levels. As applications of Markov Chain Monte Carlo (MCMC) methods, the models proposed in this paper depart from the neat assumptions of quasi-likelihood and extended quasi-likelihood, and introduce random effects models. The primary focus is the close dependency of the IBNR on data variability structures and variance models, built with reference to the generic model derived in Vera (2003). The models have been implemented in BUGS.